Nilpotent groups and biLipschitz embeddings into $L^1$

Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne +2

We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^1$ space, then it is abelian. We reach this conclusion by proving that every Carnot gr…